Probability concepts in engineering : emphasis on applications in civil & environmental engineering

Başlık:

Yazar:

Ang, Alfredo Hua-Sing, 1930-

ISBN:

9780471720645

Ek Yazar:

Ang, Alfredo Hua-Sing, 1930-

Edition:

2nd ed.

Yayım Bilgisi:

Fiziksel Tanım:

xiii, 406 pages : illustrations ; 26 cm

General Note:

Revised edition of: Probability concepts in engineering planning and design. 1975-c1984.

Contents:

Roles of probability and statistics in engineering -- Fundamentals of probability models -- Analytical models of random phenomena -- Functions of random variables -- Computer-based numerical and simulation methods in probability -- Statistical inferences from observational data -- Determination of probability distribution models -- Regression and correlation analyses -- The Bayesian approach -- Elements of quality assurance and acceptance sampling.

Konu Terimleri:

Mühendislik -- İstatistiksel yöntemler.

Engineering -- Statistical methods.

Olasılıklar.

Probabilities.

Added Author:

Tang, Wilson H.

Ang, Alfredo Hua-Sing, 1930- Probability concepts in engineering planning and design.

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Apply the principles of probability and statistics to realistic engineering problems

The material in the book is intended for a first course on applied probability and statistics for engineering students at the sophomore or junior level, or for self study, stressing probabilistic modeling and the fundamentals of statistical inferences. The primary aim is to provide an in-depth understanding of the fundamentals for the proper application in engineering problems.

The second edition of this well-known book (previously titled Probability Concepts in Engineering Planning and Design ) by Alfredo Ang and Wilson Tang, two world-renowned educators, has been revised to simplify understanding the fundamentals of probability and statistics for engineering students. The second edition includes many new and expanded topics, including hypothesis testing and confidence intervals in regression analysis. Students using this text will develop the ability to formulate and solve real-world problems in engineering. The authors accomplish this by explaining all the concepts and methods through a variety of relevant engineering and physical problems.

Each basic principle is presented and illustrated through different examples relevant to engineering and the physical sciences, particularly civil and environmental engineering. The exercise problems in each chapter further enhance understanding of basic concepts and reinforce a working knowledge of concepts and methods. The authors firmly believe that the easiest and most effective way for engineers to learn and master a new set of abstract principles is to apply them to a variety of applications.

Author Notes

ALFREDO H-S. ANG is currently Professor Emeritus of Civil and Environmental Engineering at the University of California, Irvine. He received his Ph.D. and M.S. at the University of Illinois. He received his B.S. at the Mapua Institute of Technology.

WILSON H. TANG, Chair Professor, Hong Kong University of Science & Technology.

Preface	p. vii
Chapter 1 Roles of Probability and Statistics in Engineering	p. 1
1.1 Introduction	p. 1
1.2 Uncertainty in Engineering	p. 2
1.2.1 Uncertainty Associated with Randomness-The Aleatory Uncertainty	p. 2
1.2.2 Uncertainty Associated with Imperfect Knowledge-The Epistemic Uncertainty	p. 17
1.3 Design and Decision Making under Uncertainty	p. 19
1.3.1 Planning and Design of Transportation Infrastructures	p. 20
1.3.2 Design of Structures and Machines	p. 20
1.3.3 Planning and Design of Hydrosystems	p. 22
1.3.4 Design of Geotechnical Systems	p. 23
1.3.5 Construction Planning and Management	p. 23
1.3.6 Photogrammetric, Geodetic, and Surveying Measurements	p. 24
1.3.7 Applications in Quality Control and Assurance	p. 24
1.4 Concluding Summary	p. 25
References	p. 25
Chapter 2 Fundamentals of Probability Models	p. 27
2.1 Events and Probability	p. 27
2.1.1 Characteristics of Problems Involving Probabilities	p. 27
2.1.2 Estimating Probabilities	p. 30
2.2 Elements of Set Theory-Tools for Defining Events	p. 31
2.2.1 Important Definitions	p. 31
2.2.2 Mathematical Operations of Sets	p. 39
2.3 Mathematics of Probability	p. 44
2.3.1 The Addition Rule	p. 45
2.3.2 Conditional Probability	p. 49
2.3.3 The Multiplication Rule	p. 52
2.3.4 The Theorem of Total Probability	p. 57
2.3.5 The Bayes' Theorem	p. 63
2.4 Concluding Summary	p. 65
Problems	p. 66
References	p. 80
Chapter 3 Analytical Models of Random Phenomena	p. 81
3.1 Random Variables and Probability Distribution	p. 81
3.1.1 Random Events and Random Variables	p. 81
3.1.2 Probability Distribution of a Random Variable	p. 82
3.1.3 Main Descriptors of a Random Variable	p. 88
3.2 Useful Probability Distributions	p. 96
3.2.1 The Gaussian (or Normal) Distribution	p. 96
3.2.2 The Lognormal Distribution	p. 100
3.2.3 The Bernoulli Sequence and the Binomial Distribution	p. 105
3.2.4 The Geometric Distribution	p. 108
3.2.5 The Negative Binomial Distribution	p. 111
3.2.6 The Poisson Process and the Poisson Distribution	p. 112
3.2.7 The Exponential Distribution	p. 118
3.2.8 The Gamma Distribution	p. 122
3.2.9 The Hypergeometric Distribution	p. 126
3.2.10 The Beta Distribution	p. 127
3.2.11 Other Useful Distributions	p. 131
3.3 Multiple Random Variables	p. 132
3.3.1 Joint and Conditional Probability Distributions	p. 132
3.3.2 Covariance and Correlation	p. 138
3.4 Concluding Summary	p. 141
Problems	p. 141
References	p. 150
Chapter 4 Functions of Random Variables	p. 151
4.1 Introduction	p. 151
4.2 Derived Probability Distributions	p. 151
4.2.1 Function of a Single Random Variable	p. 151
4.2.2 Function of Multiple Random Variables	p. 157
4.2.3 Extreme Value Distributions	p. 172
4.3 Moments of Functions of Random Variables	p. 180
4.3.1 Mathematical Expectations of a Function	p. 180
4.3.2 Mean and Variance of a General Function	p. 183
4.4 Concluding Summary	p. 190
Problems	p. 190
References	p. 198
Chapter 5 Computer-Based Numerical and Simulation Methods in Probability	p. 199
5.1 Introduction	p. 199
5.2 Numerical and Simulations Methods	p. 200
5.2.1 Essentials of Monte Carlo Simulation	p. 200
5.2.2 Numerical Examples	p. 201
5.2.3 Problems Involving Aleatory and Epistemic Uncertainties	p. 223
5.2.4 MCS Involving Correlated Random Variables	p. 231
5.3 Concluding Summary	p. 242
Problems	p. 242
References and Softwares	p. 244
Chapter 6 Statistical Inferences from Observational Data	p. 245
6.1 Role of Statistical Inference in Engineering	p. 245
6.2 Statistical Estimation of Parameters	p. 246
6.2.1 Random Sampling and Point Estimation	p. 246
6.2.2 Sampling Distributions	p. 255
6.3 Testing of Hypotheses	p. 258
6.3.1 Introduction	p. 258
6.3.2 Hypothesis Test Procedure	p. 259
6.4 Confidence Intervals	p. 262
6.4.1 Confidence Interval of the Mean	p. 262
6.4.2 Confidence Interval of the Proportion	p. 268
6.4.3 Confidence Interval of the Variance	p. 269
6.5 Measurement Theory	p. 270
6.6 Concluding Summary	p. 273
Problems	p. 274
References	p. 277
Chapter 7 Determination of Probability Distribution Models	p. 278
7.1 Introduction	p. 278
7.2 Probability Papers	p. 279
7.2.1 Utility and Plotting Position	p. 279
7.2.2 The Normal Probability Paper	p. 280
7.2.3 The Lognormal Probability Paper	p. 281
7.2.4 Construction of General Probability Papers	p. 284
7.3 Testing Goodness-of-Fit of Distribution Models	p. 289
7.3.1 The Chi-Square Test for Goodness-of-Fit	p. 289
7.3.2 The Kolmogorov-Smirnov (K-S) Test for Goodness-of-Fit	p. 293
7.3.3 The Anderson-Darling Test for Goodness-of-Fit	p. 296
7.4 Invariance in the Asymptotic Forms of Extremal Distributions	p. 300
7.5 Concluding Summary	p. 301
Problems	p. 302
References	p. 305
Chapter 8 Regression and Correlation Analyses	p. 306
8.1 Introduction	p. 306
8.2 Fundamentals of Linear Regression Analysis	p. 306
8.2.1 Regression with Constant Variance	p. 306
8.2.2 Variance in Regression Analysis	p. 308
8.2.3 Confidence Intervals in Regression	p. 309
8.3 Correlation Analysis	p. 311
8.3.1 Estimation of the Correlation Coefficient	p. 312
8.3.2 Regression of Normal Variates	p. 313
8.4 Linear Regression with Nonconstant Variance	p. 318
8.5 Multiple Linear Regression	p. 321
8.6 Nonlinear Regression	p. 325
8.7 Applications of Regression Analysis in Engineering	p. 333
8.8 Concluding Summary	p. 339
Problems	p. 339
References	p. 344
Chapter 9 The Bayesian Approach	p. 346
9.1 Introduction	p. 346
9.1.1 Estimation of Parameters	p. 346
9.2 Basic Concepts-The Discrete Case	p. 347
9.3 The Continuous Case	p. 352
9.3.1 General Formulation	p. 352
9.3.2 A Special Application of the Bayesian Updating Process	p. 357
9.4 Bayesian Concept in Sampling Theory	p. 360
9.4.1 General Formulation	p. 360
9.4.2 Sampling from Normal Populations	p. 360
9.4.3 Error in Estimation	p. 362
9.4.4 The Utility of Conjugate Distributions	p. 365
9.5 Estimation of Two Parameters	p. 368
9.6 Bayesian Regression and Correlation Analyses	p. 372
9.6.1 Linear Regression	p. 372
9.6.2 Updating the Regression Parameters	p. 374
9.6.3 Correlation Analysis	p. 375
9.7 Concluding Summary	p. 377
Problems	p. 377
References	p. 381
Chapter 10 Elements of Quality Assurance and Acceptance Sampling
Appendices
Appendix A Probability Tables	p. 383
Table A.1 Standard Normal Probabilities	p. 383
Table A.2 CDF of the Binomial Distribution	p. 387
Table A.3 Critical Values of t-Distribution at Confidence Level (1-[alpha]) = p	p. 392
Table A.4 Critical Values of the x[superscript 2] Distribution at probability Level [alpha]	p. 393
Table A.5 Critical Values of D[superscript alpha subscript n] at Significance Level [alpha] in the K-S Test	p. 395
Table A.6 Critical Values of the Anderson-Darling Goodness-of-Fit Test	p. 395
Appendix B Combinatorial Formulas	p. 397
B.1 The Basic Relation	p. 397
B.3 The Binomial Coefficient	p. 398
B.4 The Multinomial Coefficient	p. 399
B.5 Stirling's Formula	p. 399
Appendix C Derivation of the Poisson Distribution	p. 400
Index	p. 403

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